\relax 
\@writefile{toc}{\contentsline {chapter}{{Acknowledgements}}{ii}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{lop}{\addvspace {10\p@ }}
\citation{BuhlerReichstein1997On-the-essentia}
\citation{Reichstein2000On-the-notion-o}
\citation{BrosnanReichsteinVistoli2007Essential-dimen}
\citation{BerhuyFavi2003Essential-dimen}
\citation{BuhlerReichstein1997On-the-essentia}
\citation{KemperMattig2000Generic-polynom}
\citation{JensenLedetYui2002Generic-polynom}
\@writefile{toc}{\contentsline {chapter}{\numberline {1}{Introduction}}{1}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{lop}{\addvspace {10\p@ }}
\newlabel{chap:intro}{{1}{1}}
\citation{Manin1967Rational-surfac}
\citation{Iskovskih1979Minimal-models-}
\citation{Serre2008Le-group-de-cre}
\citation{Tokunaga2006Two-dimensional}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{Wiman1896Zur_Thorie_der_}
\citation{BayleBeauville2000Birational_invo}
\citation{deFernex2004On_planar_Cremo}
\citation{Zhang2001Automorphisms-o}
\citation{Beauville2007p-elementary-su}
\citation{Blanc2007Finite-abelian-}
\citation{Prokhorov2009Simple-finite-s}
\@writefile{toc}{\contentsline {section}{\numberline {1.1}{Essential Dimension via Birational Geometry}}{2}}
\newlabel{sec:EDviaBG}{{1.1}{2}}
\citation{Ledet2007Finite-groups-o}
\citation{ChuHuKangZhang2008Groups_with_ess}
\citation{KarpenkoMerkurjev2008Essential-dimen}
\citation{MeyerReichstein2008Some_consequenc}
\citation{KraftSchwarz2007Compression-of-}
\citation{KraftLotscherSchwarz2009Compression-of-}
\citation{Reichstein2004Compressions-of}
\citation{Lotscher2008Application-of-}
\@writefile{toc}{\contentsline {section}{\numberline {1.2}{Finite Groups of Essential Dimension $2$}}{3}}
\newlabel{sec:ed2intro}{{1.2}{3}}
\newlabel{thm:ed2classification}{{1.1}{3}}
\newlabel{thm:ed2:GL2}{{1}{3}}
\citation{Cox1995The-homogeneous}
\citation{ColliotTheleneSansuc1987La_descente_sur}
\newlabel{thm:ed2:G1}{{2}{4}}
\newlabel{thm:ed2:G2}{{3}{4}}
\newlabel{thm:ed2:G3}{{4}{4}}
\newlabel{thm:ed2:G4}{{5}{4}}
\newlabel{thm:ed2:PSL27}{{6}{4}}
\newlabel{thm:ed2:S5}{{7}{4}}
\newlabel{thm:ed2to4surfaces}{{1.2}{4}}
\citation{BuhlerReichstein1997On-the-essentia}
\citation{Serre2008Le-group-de-cre}
\citation{Prokhorov2009Simple-finite-s}
\@writefile{toc}{\contentsline {section}{\numberline {1.3}{Essential Dimension of $A_7$ and $S_7$}}{5}}
\newlabel{sec:edS7intro}{{1.3}{5}}
\newlabel{thm:edS7}{{1.3}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {1.4}{Overview}}{5}}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}{Del Pezzo Surfaces of Degree $\le 4$}}{7}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{lop}{\addvspace {10\p@ }}
\newlabel{chap:DelPezzo}{{2}{7}}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{Hartshorne1977Algebraic-geome}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{Manin1986Cubic-forms}
\@writefile{toc}{\contentsline {section}{\numberline {2.1}{Alternative Proofs}}{9}}
\newlabel{sec:altProofs}{{2.1}{9}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.1}{Del Pezzo Surfaces of Degree $4$}}{9}}
\newlabel{thm:DP4Versal}{{2.1}{9}}
\newlabel{lem:ed2inWD5}{{2.2}{9}}
\citation{Segre1942The-Non-singula}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{Hosoh1997Automorphism-grou}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.2}{Del Pezzo Surfaces of Degree $3$}}{10}}
\newlabel{thm:DP3Versal}{{2.3}{10}}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{Iskovskih1979Minimal-models-}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\newlabel{lem:minMonomialExp}{{2.4}{11}}
\newlabel{lem:cubicReducible}{{2.5}{11}}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\citation{Kraft2006A_result_of_Her}
\newlabel{lem:cubicNo5}{{2.6}{12}}
\newlabel{lem:cubicMonoVersal}{{2.7}{13}}
\citation{Serre1977Linear-represen}
\newlabel{lem:cubicIrred}{{2.8}{15}}
\citation{DolgachevIskovskikh2006Finite-subgroup}
\newlabel{lem:A2toFermat}{{2.9}{16}}
\citation{BuhlerReichstein1997On-the-essentia}
\citation{BuhlerReichstein1999On-Tschirnhaus-}
\citation{Dixmier1993Hilbert}
\citation{Arnold1957}
\citation{Kolmogorov1957}
\citation{Saltman1982Generic_Galois_}
\citation{DeMeyer1983Generic_polynom}
\citation{KemperMattig2000Generic-polynom}
\citation{JensenLedetYui2002Generic-polynom}
\@writefile{toc}{\contentsline {chapter}{\numberline {3}{Conclusion}}{18}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{lop}{\addvspace {10\p@ }}
\newlabel{chap:conclusion}{{3}{18}}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}{Applications}}{18}}
\citation{Saltman1982Generic_Galois_}
\citation{Coray1987Cubic_hypersurf}
\citation{ReichsteinYoussin2002Conditions_sati}
\citation{Kraft2006A_result_of_Her}
\citation{ReichsteinYoussin2002A-birational-in}
\citation{BannaiTokunaga2007A-note-on-embed}
\citation{Iskovskikh2003Two_nonconjugat}
\@writefile{toc}{\contentsline {section}{\numberline {3.2}{Future Research}}{19}}
\citation{Serre2008Le-group-de-cre}
\citation{BerhuyFavi2003Essential-dimen}
\citation{Prokhorov2009Simple-finite-s}
\citation{Serre2009A-Minkowski-sty}
\citation{Beauville2011On_finite_simpl}
\citation{ColKunPopZin2009Is_the_function}
\bibstyle{plain}
\bibdata{bibliography}
\newlabel{conj:versalByPGroups}{{3.4}{21}}
